One-Dimensional Robust Chaotic Map and the Construction of S-Box

HAN Dan-dan; MIN Le-quan; ZHAO Geng; ZHANG Li-jiao; YAN Shi-jie

doi:10.3969/j.issn.0372-2112.2015.09.014

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One-Dimensional Robust Chaotic Map and the Construction of S-Box

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- One-Dimensional Robust Chaotic Map and the Construction of S-Box
- Acta Electronica Sinica Vol. 43, Issue 9, Pages: 1770-1775(2015)
- 作者机构：
  
  1. 北京科技大学自动化学院,北京,100083
  2. 北京科技大学数理学院,北京,100083
  3. 北京电子科技学院,北京,100070
  4. 北京科技大学自动化学院,北京,100083
  5. 北京科技大学数理学院,北京,100083
  6. 北京电子科技学院,北京,100070
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61074192, No.61170037)
- DOI：10.3969/j.issn.0372-2112.2015.09.014
  CLC： TP393
- Published：2015
- 稿件说明：
移动端阅览
HAN Dan-dan, MIN Le-quan, ZHAO Geng, et al. One-Dimensional Robust Chaotic Map and the Construction of S-Box[J]. Acta Electronica Sinica, 2015, 43(9): 1770-1775.
DOI：

HAN Dan-dan, MIN Le-quan, ZHAO Geng, et al. One-Dimensional Robust Chaotic Map and the Construction of S-Box[J]. Acta Electronica Sinica, 2015, 43(9): 1770-1775. DOI： 10.3969/j.issn.0372-2112.2015.09.014.

摘要

本文利用Li-York混沌判别定理

构造了一类分段线性连续混沌映射.基于此类映射

建立了一个构造一类分段非线性鲁棒混沌映射的判别定理.作为应用

构造了一个由多项式函数和三角函数映射合成的分段非线性鲁棒混沌映射.通过计算该混沌映射的分岔图

验证了映射在参数范围内的混沌性.作为鲁棒混沌的应用

设计了三个基于分段非线性鲁棒混沌映射的伪随机数发生器.在此基础上

利用混沌映射对初始参数的敏感性

提出了批量生成S盒的算法.S盒密码性能的分析结果表明

生成的S盒具有良好的密码学性能

可以较好的抵抗线性与差分攻击

为密码算法的研究发展提供基础与条件.

Abstract

Using the judgment theorem of Li-York chaos

this paper generates a class of piecewise linear chaotic maps.Based on the chaotic maps

a constructing theorem of piecewise nonlinear robust chaotic map is proposed.As an application

this theorem is used to construct a piecewise nonlinear robust chaotic map with a polynomial function and a trigonometric function.This study computes the bifurcation diagram of the map.The computed results demonstrate the chaotic robustness features of the map.Three pseudo-random number generators are generated based on the piecewise nonlinear robust chaotic map.On this basis

the generation algorithm of S-boxes is proposed with the property of sensitivity to the initial parameters of the chaotic map.The cryptography performance is tested and the tested results show that generated S-boxes have good cryptographic properties

and can not only better resist the linear and differential attacks

but also provide the foundation and conditions for the research and development of cryptography.

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